Roger Bainbridge has not been seen since taking a day-trip boat for the Greek island of Antipaxos, which has an area of 2 sq miles (5 sq km), on Thursday 24th September.
The 67-year-old had been staying at his sister's holiday home on the larger neighbouring island of Paxos.
A helicopter search of the island is currently being undertaken.
Roger is an experienced fell walker from the Lake District.
He was wearing walking shoes, slate blue t shirt, navy blue rucksack. He had drinking water with him.
He was last seen near the main village at the top of Antipaxos at 15.00 by some other walkers who had a conversation with him and walked with him a short way.
He has no mobile phone with him.
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